Tabular reasoning involves interpreting natural language queries about tabular data, which presents a unique challenge of combining language understanding with structured data analysis. Existing methods employ either textual reasoning, which excels in semantic interpretation but struggles with mathematical operations, or symbolic reasoning, which handles computations well but lacks semantic understanding. This paper introduces a novel algorithm H-STAR that integrates both symbolic and semantic (textual) approaches in a two-stage process to address these limitations. H-STAR employs: (1) step-wise table extraction using `multi-view' column retrieval followed by row extraction, and (2) adaptive reasoning that adapts reasoning strategies based on question types, utilizing semantic reasoning for direct lookup and complex lexical queries while augmenting textual reasoning with symbolic reasoning support for quantitative and logical tasks. Our extensive experiments demonstrate that H-STAR significantly outperforms state-of-the-art methods across three tabular question-answering (QA) and fact-verification datasets, underscoring its effectiveness and efficiency.